Mathematical Physics Seminar

We consider the point spectrum of non-selfadjoint Dirac operators which arise as linearizations at solitary wave solutions to the nonlinear Dirac equation. We prove that in the nonrelativistic limit (\omega\lesssim m) the solitary waves in the Dirac equation with scalar-type self-interaction ("Soler model") with "NLS-subcritical" nonlinearity are spectrally stable. The results are obtained together with Nabile Boussaid, University of Bourgogne -- Franche-Comte and are partially based on articles "On spectral stability of the nonlinear Dirac equation" (with Nabile Boussaid), JFA-2016, http://arxiv.org/abs/1211.3336 "Nonrelativistic asymptotics of solitary waves in the Dirac equation with the Soler-type nonlinearity" (with Nabile Boussaid), http://arxiv.org/abs/1606.07308